Directions

Add the beef to the marinade, making sure each piece is coated with the mixture. Transfer the meat and the marinade to a quart-size freezer bag. Seal and refrigerate for at least 8 hours or preferably overnight. Allow the meat to come to room temperature before cooking, about 30 minutes. Remove the meat from the marinade and pat dry with paper towels. Discard the marinade.

In a large heavy pot, heat the vegetable oil over medium-high heat. Sear the meat on all sides, a few pieces at a time, about 4 minutes per side. Transfer the browned meat to a platter and set aside.

Add the onions, peppers, garlic, and chiles to the hot pan. Saute for 5 minutes, then add the beef broth, tomatoes, oregano, salt and pepper, to taste. Mix well, then return the meat to the pan. Bring to a boil, reduce the heat, cover, and simmer slowly until the meat is very tender, about 2 hours. Transfer the meat to a cutting board and allow to rest until cool enough to handle, about 15 minutes. Continue to cook the onion mixture until most of the liquid has evaporated, about 10 minutes.

Using your fingers or 2 forks, shred the meat into 2-inch-long pieces. Return the shredded meat to the pot, stir to combine, and cook until meat is very hot, about 3 minutes.

Warm the tortillas over a burner or in a dry skillet over medium heat for 20 seconds. Put about 2 tablespoons of the meat mixture in the center of each tortilla, and roll into a thin burrito. Arrange them on a serving platter and garnish with lime wedges.